On global stability of the intra-host dynamics of malaria and the immune system

AbstractIn this paper we consider an intra-host model for the dynamics of malaria. The model describes the dynamics of the blood stage malaria parasites and their interaction with host cells, in particular red blood cells (RBC) and immune effectors. We establish the equilibrium points of the system and analyze their stability using the theory of competitive systems, compound matrices and stability of periodic orbits. We established that the disease-free equilibrium is globally stable if and only if the basic reproduction number satisfies R0⩽1 and the parasite will be cleared out of the host. If R0>1, a unique endemic equilibrium is globally stable and the parasites persist at the endemic steady state. In the presence of the immune response, the numerical analysis of the model shows that the endemic equilibrium is unstable

Prevalence of child injuries in Mbale region, Eastern Uganda

Background: The rate of unintentional child injuries in sub-Saharan Africa is at 53.1 per 100,000, The highest for low income regions, data on these injuries and associated factors among children in Uganda is very scanty. Most child injuries are related to the way of life in rural communities typically burns from charcoal stoves, candle light , hot fluids, chemicals , falls, and animal bites .Methods: This was a cross sectional community survey among the Promise EBF participants in Mbale district of east Uganda.Objective; to establish the prevalence, causes and associated factors of un intentional child injuries in Mbale District .Results: The commonest unintentional injuries were, falls, and burns 11% of the children. The main causes were hot water (43%) and burning charcoal stoves/firewood. Predisposing factors to burns were residence in rural areas (OR 2.0; 95% CI: 1.1, 3.5) and having three or more siblings (OR 1.6; 95% CI: 0.9, 2.8) .. 40% of the well off mothers and those with at least 8 years of education were more likely to report their child injuries. ((OR: 1.7; 95% CI 1.0, 2.9) and (OR 1.5; 95% CI 1.0, 2.2) respectively).Conclusion: The prevalence of unintentional injuries among children of this cohort of mothers was high, caused by burns, falls, poisoning and animal bites

Variable effect of co-infection on the HIV infectivity: Within-host dynamics and epidemiological significance

<p>Abstract</p> <p>Background</p> <p>Recent studies have implicated viral characteristics in accounting for the variation in the HIV set-point viral load (spVL) observed among individuals. These studies have suggested that the spVL might be a heritable factor. The spVL, however, is not in an absolute equilibrium state; it is frequently perturbed by immune activations generated by co-infections, resulting in a significant amplification of the HIV viral load (VL). Here, we postulated that if the HIV replication capacity were an important determinant of the spVL, it would also determine the effect of co-infection on the VL. Then, we hypothesized that viral factors contribute to the variation of the effect of co-infection and introduce variation among individuals.</p> <p>Methods</p> <p>We developed a within-host deterministic differential equation model to describe the dynamics of HIV and malaria infections, and evaluated the effect of variations in the viral replicative capacity on the VL burden generated by co-infection. These variations were then evaluated at population level by implementing a between-host model in which the relationship between VL and the probability of HIV transmission per sexual contact was used as the within-host and between-host interface.</p> <p>Results</p> <p>Our within-host results indicated that the combination of parameters generating low spVL were unable to produce a substantial increase in the VL in response to co-infection. Conversely, larger spVL were associated with substantially larger increments in the VL. In accordance, the between-host model indicated that co-infection had a negligible impact in populations where the virus had low replicative capacity, reflected in low spVL. Similarly, the impact of co-infection increased as the spVL of the population increased.</p> <p>Conclusion</p> <p>Our results indicated that variations in the viral replicative capacity would influence the effect of co-infection on the VL. Therefore, viral factors could play an important role driving several virus-related processes such as the increment of the VL induced by co-infections. These results raise the possibility that biological differences could alter the effect of co-infection and underscore the importance of identifying these factors for the implementation of control interventions focused on co-infection.</p

On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number, R0 is less than unity. We also note that when R0>1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state

Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits

In this paper, we develop and analyze a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission, and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters R0 and R over bar 01, the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub-critical (backward) bifurcation is possible at R0=1. Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa